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Simplifying w = 4w2 + 10 Reorder the terms: w = 10 + 4w2 Solving w = 10 + 4w2 Solving for variable 'w'. Reorder the terms: -10 + w + -4w2 = 10 + 4w2 + -10 + -4w2 Reorder the terms: -10 + w + -4w2 = 10 + -10 + 4w2 + -4w2 Combine like terms: 10 + -10 = 0 -10 + w + -4w2 = 0 + 4w2 + -4w2 -10 + w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 -10 + w + -4w2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.5 + -0.25w + w2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -0.25w + -2.5 + w2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -0.25w + w2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -0.25w + w2 = 0 + -2.5 -0.25w + w2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -0.25w + w2 = -2.5 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.25w + 0.25 + w2 = -2.5 + 0.25 Reorder the terms: 0.25 + -0.25w + w2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 0.25 + -0.25w + w2 = -2.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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